UNIT 2

# Pharmaceutical Calculations:

Weight and measures

There are 2 systems of weight and measures,
Imperial system
Metric system

Imperial system:-
Avoirdupois system– Pound is the standard unit for weighting all measures of all mass are derived from it.(1 pound = 5760 grains)
Apothecaries system (Troy stem) – Grain is the standard unit in this system

Metric system:-

Measurement of weight – Kilogram is the standard unit of measurement(1 kg= 100 gm)
Measurement of capacity – liter is the standard unit of measurement (1 L = 100 ml)

## Calculations involving % solutions:-

Calculate the amt. of 95% alcohol required to prepare 400 ml of 45% alcohol.
Vol. req. = 400 ml, % alcohol required= 45%, % alcohol used= 95%
Vol. of strong alcohol to be used = vol. required * % required / % used
= 400*45/95
=184.47 ml

### Alligation Method:-

When calculations involve mixing of 2 similar preparations of diff. strength, to produce a preparation of intermediate strength, the alligation method is used.
Calculate the volume of 95 % alcohol required to prepare 600 ml of 70 % alcohol
Vol. required = 600 ml, % alcohol required = 70, % alcohol used = 95
70 parts of 95% alcohol & 25 parts water will produce the required % alcohol
Qty of 95% alcohol req. = 600*70/ 95 = 422.10 ml
Qty of water req. = 600*25/95 = 157.90 ml

Proof spirit Calculation:-
The strength of alcohol is calculated in proof degree. As per Indian standards 100% proof spirit = 57% v/v ethyl alcohol
The value of more than 57 % = overproof spirit
The value less than 57 % = under a proof spirit
Calculate the proof strength of 95% v/v alcohol.
Proof strength= % strength of alcohol* 1.753-100
=95*1.753-100
= 66.53° O.P

Isotonic solution:-
The solutions having same osmotic pressure or equal solute concentration is called an isotonic solution.
Freezing point:-
% w/v of adjusting substance needed = 0.52-PSM*a / b
Where, PSM= percentage strength of the measurement
A= freezing point of the unadjusted solution
B =freezing point of 1% w/v sol. of adjusted solution

Molecular weight:-
% w/v of adjusting substance needed = 0.03M/N
Where M= gram molecular weight
N= no. of ions into which substance is ionized

###### Pharmaceutical Calculations Notes

Powders:-
A solid dosage form consisting of a mixture of dry, finely divided drugs and chemicals intended for internal or external use. It is used as a basis of solid dosage forms such as tablets, capsules, etc.

### Classification:-

1. Bulk powders for external use:
(a) Dusting powders – applied externally for local application
(b) Snuffs – inhaled into nostrils during decongestion
(c) Dental powder – used for cleaning teeth surface
(d) Insufflations – applied in body cavities as ear, nose, vagina, etc

2. Bulk powders for internal use. – a non- potent drug used as an antacid, laxative, purgative, etc.
3. Simple and compound powders for internal use – unit dose powders packed in papers and dispensed in envelopes, metal foils, plastic bags, etc.
4. Effervescent granules – In salt or granule form which react in presence of water evolving co2.
5. Eutectic mixtures–  the composition of at least two solid components that produces a change of phase to liquid at a certain temperature.
6. Cachets – made of flour and water which get easily damaged, so replaced by Capsules.

•  There is a wide choice of ingredients, and dose can easily be achieved for patient administration.
•  Have better physicochemical stability and longer shelf life compared to liquid dosage forms.
•  Children and adults who have trouble swallowing tablets or capsules may find powders more acceptable.
• A large dose that cannot be administered in other forms can be administered as powder.
•  Rapid dispersion of drugs occurs in the stomach.
• The dissolution rate of oral powders containing water-soluble drugs is generally faster than tablets or capsules,
• in which disintegration of the tablet or the capsule shell is required prior to dissolution.
• A powder can be dispersed in water or another liquid and more easily swallowed.
• Economic dosage form.
• Offer a lot of flexibility in compounding solids.

• Powders are not the dosage form of choice for drugs with an unpleasant taste.
• Drugs that deteriorate rapidly with exposure to the atmosphere or acidic pH should not be dispensed as powders.
• Powders are bulky and inconvenient to carry.
• Powders are not a suitable dosage form for the administration of drugs that are inactivated in the stomach or
• drugs that can cause damage to the stomach.
• Dispensing potent drugs requiring low doses as powders (e.g., bulk powders) may not be appropriate.
• Powders are not well suited for dispensing hygroscopic or deliquescent drugs.
###### Pharmaceutical Calculations Notes

Simple powders:- It consists of only one active ingredient either in crystalline or amorphous form. If the powder is in a crystalline form then it is reduced to fine powders, Supplied in a single dose packet separately
For example:
Rx
Paracetamol …500mg

Compound powders:- It consists of a mixture of more than one active ingredient and constituents and each dose is supplied in a single packet.
For example:
Rx
Aspirin 250mg
Paracetamol 150mg
Caffeine 50mg

Dusting Powder:- Dusting powders are fine medicinal (bulk) powders intended to be dusted on the skin by means of sifter-top containers. A single medicinal agent is used as a dusting powder and passes through a 100-200 mesh sieve.

Effervescent Powder:– This preparation can be supplied either by compounding the ingredients as granules or dispensed in the form of salts. They react in presence of water-evolving carbon dioxide gas.
Chemical reaction
3 NaHC03 + C6H807.H20 = C6H5Na307 + 3 C02 + 3 H20 (Sodium bicarbonate) (Citric acid)

Efflorescent powders:- Some crystalline substances liberate water of crystallization on exposure to the humid atmosphere or during trituration and thus become wet or liquefy. (Ex. caffeine, citric acid, ferrous sulfate, etc)
Hygroscopic powders: The powders which absorb moisture from the atmosphere are called hygroscopic powders. Such substances are usually supplied in granular form in order to expose less surface area to the atmosphere. (Ex. Halides and alkaloids)
Eutectic mixtures: Mixture of substances that liquefy when mixed, rubbed, or triturated together. The melting points of many eutectic mixtures are below room temp. (Ex. menthol, thymol, phenol, camphor)
Geometric Dilution:-
The geometric dilution method is used when potent substances are too mixed with a large number of diluents. The potent drug is placed upon an approximately equal volume of the dilute in a mortar and the substances are slightly mixed by trituration. The second portion of diluents equal in volume to the powder mixture in the mortar is added and trituration is repeated. The process is continued by adding diluents equal in volume to the mixture in the mortar at each step until all the diluents are incorporated.

For example, if 100mg of the potent drug is required to be mixed with 900mg of lactose then according to geometric dilution, the following procedure should be followed:-
100mg of potent drug + 100mg of lactose = 200mg of mixture
200mg of the mixture + 200 mg of lactose= 400 mg of mixture
400mg of the mixture + 400mg of lactose =800mg of mixture
800mg of the mixture + remaining portion = 1000mg of mixture of lactose

###### Pharmaceutical Calculations Notes

LIQUID DOSAGE FORM:-
The liquid form of a drug dose for administration or consumption. Route of administration may be oral, intravenous, intramuscular, cutaneous, subcutaneous, etc.

• Most suitable dosage form for patients who have difficulty taking tablets or capsules, as might be the case with pediatric or geriatric patients.
• Attractive in appearance gives beneficial psychological effects.
• Drugs with bitter unpleasant taste can be given in sweetened, colored, flavored vehicles.
• Measuring flexibility as needed.
• If given orally, the liquid dosage is rapidly absorbed than tablets and capsules.
• Hygroscopic and deliquescent medicaments can easily be given in liquid dosage form.
• products like adsorbents and antacids are more effective in this form.
• The liquid dosage form is expected for products like cough medicaments.

Liquid dosage forms are usually more susceptible to chemical degradation when compared to solid dosage forms.

• Inconvenient to transport and store.
• Accidental breakage of the container results in loss of whole dosage form.
• The shelf-life of a liquid dosage form is often much shorter than that of solid preparation due to low stability.
• The solution often provides suitable media for microbial growth.
• Liquid dosage forms e.g. vaccines may require special storage conditions
• The taste of a drug that is usually unpleasant is more prominent in solution form.
• There is a higher chance of dose variability since the delivery of the dose depends upon the patient measuring the proper volume. This can be a significant issue for patients with vision-impaired, arthritis, unable to read the numbers on measuring cups.

### Excipients used in formulation-

Vehicles= vehicles are major components used as a base in which drugs and other excipients are dissolved or dispersed.
Aqueous– (e.g. Water, polyhydric alcohols, hydro-alcoholic solutions, and buffers)
Oily- (e.g. Vegetable or mineral oils, organic oily bases, emulsified bases, etc.),
Buffers= Buffers are added to regulate the pH when an acid or alkali is added to the liquid dosage form. (e.g. Monobasic sodium acetate, sodium citrate, potassium phosphate, etc)
Tonicity modifier= to make the solution iso-osmotic with tissue fluid to avoid pain and irritation (e.g. dextrose, NaCl)
Preservatives= preservatives are added for fungistatic action to avoid microbial growth in the formulation. (E.g. benzoic acid, sod. Benzoate, alcohol, propylparaben, methylparaben)
Antioxidant= antioxidants are used to prevent oxidation which may lead to unpleasant taste, odor, taste, precipitation, discoloration, or even loss of activity. (E.g. sod. Sulfite, sod. Bisulfite, ascorbic acid, citric acid)
Viscosity modifier= Used to minimize interparticle attraction and aggregation by functioning as energy barrier thus retarding particle settling. (e.g.  methylcellulose, microcrystalline cellulose, carboxymethylcellulose, etc)
Sweetening agent= Used to mask the bitter taste of the formulation (e.g. sucrose, sorbitol, mannitol, glycerol)
Flavors & perfumes = Used to give a specific flavor to improve patient compatibility. (e.g. cinnamon oil, lemon oil, peppermint oil)
Colours= Used to improve the attractiveness of the product and easy identification of the formulation. (e.g. Amaranth sol.-RED, tartrazine sol.- YELLOW,)

### Solubility enhancement Techniques:-

Strongly ionized drugs are freely soluble in water over a wide pH range, for unionized drugs/weak electrolytes at pH that is unfavorable for extensive ionization some techniques can be used to improve aq. Solubility,
Cosolvency = Solubility of poorly soluble drugs can be improved by using cosolvents, cosolvents are a mixture of water and one or more water-miscible solvents.
pH control= The solubility of the weak base can be increased by lowering pH & the solubility of weak acid increased by increasing pH.
Solubilization=By addition of surface-active agents micelle is formed. Non-polar molecules will dissolve in lipophilic moiety and hydrophilic surfactant HLB value above 15 is valuable as solubilizing agents.
Hydrotropy= Addition of large amt. of a second solute increase aq. Solubility of existing solute.
Particle size reduction=As a particle size is reduced using micronization technique the surface area increases and that allows greater interaction with a solvent which causes increase insolubility.
Nanonization= Improves the dissolution and bioavailability of numerous drugs which are poorly soluble in water. A technique used is wet milling, homogenization, spray drying, etc.
Solid dispersion= It increases dissolution, absorption & therapeutic efficacy of a drug. Solid dispersion is a group of solid products consisting of at least 2 diffs. components as hydrophilic matrix and hydrophobic drugs.
Complexation= Complexation of drugs with cyclodextrins has been used to enhance aq. Solubility and drug stability. It relies on relatively weak forces such as London forces, hydrogen bonding & hydrophobic interactions.

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